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Chapter 3 Stoichiometry: Calculations with Chemical Formulas and Equations

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## Chapter 3 Stoichiometry: Calculations with Chemical Formulas and Equations

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**Chapter 3Stoichiometry:Calculations with Chemical Formulas**and Equations**Law of Conservation of Mass**“We may lay it down as an incontestable axiom that, in all the operations of art and nature, nothing is created; an equal amount of matter exists both before and after the experiment. Upon this principle, the whole art of performing chemical experiments depends.” --Antoine Lavoisier, 1789**Chemical Equations**Chemical equations are concise representations of chemical reactions.**Anatomy of a Chemical Equation**CH4(g) + 2O2(g) CO2(g) + 2H2O(g) Reactants appear on the left side of the equation. Products appear on the right side of the equation. Coefficients are inserted to balance the equation.**Subscripts and Coefficients Give Different Information**• Subscripts tell the number of atoms of each element in a molecule. • Coefficients tell the number of molecules.**Combination Reactions**2Mg(s) + O2(g) 2MgO(s) N2(g) + 3H2(g) 2NH3(g) C3H6(g) + Br2(l) C3H6Br2(l) In combination reactions two or more substances react to form one product.**Decomposition Reactions**In a decomposition reaction one substance breaks down into two or more substances. Decomposition of sodium azide, NaN3(s), is used to inflate automobile air bags. CaCO3(s) CaO(s) + CO2(g) 2KClO3(s) 2KCl(s) + O2(g) 2NaN3(s) 2Na(s) + 3N2(g)**Sample Exercise 3.3Writing Balanced Equations for**Combination and Decomposition Reactions Write a balanced equation for (a) the combination reaction between lithium metal and fluorine gas and (b) the decomposition reaction that occurs when solid barium carbonate is heated (two products form, a solid and a gas). Solution: (a) 2Li(s) + F2(g) 2LiF(s) (b) BaCO3(s) BaO(s) + CO2(g)**Combustion Reactions**CH4(g) + 2O2(g) CO2(g) + 2H2O(g) C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(g) Combustion reactions are generally rapid reactions that produce a flame. Combustion reactions most often involve hydrocarbons reacting with oxygen in the air.**Sample Exercise 3.4Writing Balanced Equations for Combustion**Reactions Write the balanced equation for the reaction that occurs when methanol,CH3OH(l), is burned in air. Solution: CH3OH(l) + O2(g) CO2(g) + 2H2O(g) • CH3OH(l) + O2(g) CO2(g) + H2O(g) • CH3OH(l) + 3/2O2(g) CO2(g) + 2H2O(g) • 2CH3OH(l) + 3O2(g) CO2(g) + 4H2O(g)**Formula Weight (FW)**• A formula weight is the sum of the atomic weights for the atoms in a chemical formula. • So, the formula weight of calcium chloride, CaCl2, would be Ca: 1(40.08 amu) + Cl: 2(35.453 amu) 110.99 amu • Formula weights are generally reported for ionic compounds.**Molecular Weight (MW)**• A molecular weight is the sum of the atomic weights of the atoms in a molecule. • For the molecule ethane, C2H6, the molecular weight would be C: 2(12.011 amu) + H: 6(1.00794 amu) 30.070 amu**(number of atoms)(atomic weight)**x 100 % Element = (FW of the compound) Percent Composition One can find the percentage of the mass of a compound that comes from each of the elements in the compound by using this equation:**(2)(12.011 amu)**%C = (30.070 amu) 24.022 amu = x 100 30.070 amu = 79.887% Percent Composition So the percentage of carbon in ethane (C2H6) is:**Avogadro’s Number**• 6.02 x 1023 • 1 mole of 12C has a mass of 12.000 g.**Molar Mass**By definition, a molar mass is the mass of 1 mol of a substance (i.e., g/mol). The molar mass of an element is the mass number for the element that we find on the periodic table. The formula weight (in amu’s) will be the same number as the molar mass (in g/mol).**Using Moles**Moles provide a bridge from the molecular scale to the real-world scale.**Mole Relationships**• One mole of atoms, ions, or molecules contains Avogadro’s number of those particles. • One mole of molecules or formula units contains Avogadro’s number times the number of atoms or ions of each element in the compound.**Calculating Empirical Formulas**One can calculate the empirical formula from the percent composition.**Calculating Empirical Formulas**The compound para-aminobenzoic acid (you may have seen it listed as PABA on your bottle of sunscreen) is composed of carbon (61.31%), hydrogen (5.14%), nitrogen (10.21%), and oxygen (23.33%). Find the empirical formula of PABA. Assuming 100.00 g of para-aminobenzoic acid, C: 61.31 g x = 5.105 mol C H: 5.14 g x = 5.09 mol H N: 10.21 g x = 0.7288 mol N O: 23.33 g x = 1.456 mol O 1 mol 12.01 g 1 mol 1.01 g 1 mol 14.01 g 1 mol 16.00 g**5.105 mol**0.7288 mol C: = 7.005 7 H: = 6.984 7 N: = 1.000 O: = 2.001 2 5.09 mol 0.7288 mol 0.7288 mol 0.7288 mol 1.458 mol 0.7288 mol Calculating Empirical Formulas Calculate the mole ratio by dividing by the smallest number of moles: These are the subscripts for the empirical formula: C7H7NO2**Combustion Analysis**Compounds containing C, H, and O are routinely analyzed through combustion in a chamber like the one shown in Figure 3.14. C is determined from the mass of CO2 produced. H is determined from the mass of H2O produced. O is determined by difference after the C and H have been determined.**Stoichiometric Calculations**The coefficients in the balanced equation give the ratio of moles of reactants and products.**Starting with the mass of Substance A, you can use the ratio**of the coefficients of A and B to calculate the mass of Substance B formed (if it’s a product) or used (if it’s a reactant).**C6H12O6 + 6 O2 6 CO2 + 6 H2O**Starting with 1.00 g of C6H12O6… we calculate the moles of C6H12O6… use the coefficients to find the moles of H2O… and then turn the moles of water to grams.**Limiting Reactants**• The limiting reactant is the reactant present in the smallest stoichiometric amount. In other words, it’s the reactant you’ll run out of first (in this case, the H2). The O2 would be the excess reagent.**Theoretical Yield**• The theoretical yield is the maximum amount of product that can be made. • In other words, it’s the amount of product possible as calculated through the stoichiometry problem. • This is different from the actual yield, which is the amount one actually produces and measures.**actual yield**theoretical yield Percent yield = x 100 Percent Yield One finds the percent yield by comparing the amount actually obtained (actual yield) to the amount it was possible to make (theoretical yield):